The paper describes aspects of the statistical content knowledge of 46 preservice elementary school teachers. The preservice teachers responded to a written item designed to assess their knowledge of mean, median, and mode. The data produced in response to the written item were examined in light of the Structure of the Observed Learning Outcome (SOLO) Taxonomy (Biggs & Collis, 1982) and Ma's (1999 conception of Profound Understanding of Fundamental Mathematics (PUFM). Four levels of thinking in regard to comparing and contrasting mean, median, and mode are described. Several different categories of written definitions for each measure of central tendency are also described. Connections to previous statistical thinking literature are discussed, implications for teacher education are given, and directions for further research are suggested.Preservice Elementary Teachers' Conceptual and Procedural Knowledge of Mean, Median, and Mode Shulman (1987) used the term "content knowledge" to describe knowledge of the structure and methods of discourse within any given discipline. He stated that the many aspects of content knowledge "are properly understood as a central feature of the knowledge base of teaching" (p. 9). Research illustrates that attaining content knowledge is an important part of a mathematics teacher's development (Putnam, Heaton, Prawat, & Remillard, 1992). At the same time, research illustrates that teachers sometimes lack the content knowledge they need in order to teach elementary school mathematics (Ma, 1999). Ball, Lubienski, and Mewborn (2001) argued that Without such (mathematical) knowledge, teachers lack resources necessary for solving central problems in their workfor instance, using curriculum materials judiciously, choosing and using representations and tools, skillfully interpreting and responding to their students' work, and designing useful homework assignments (p. 433).The statistical measures of mean, median, and mode comprise a fundamental portion of the content knowledge elementary teachers need to possess. Curriculum documents around the world recommend that students develop some understanding of mean, median, and mode before entering secondary school (Australian Education Council, 1994; School Curriculum and Assessment Authority & Curriculum and Assessment Authority for Wales, 1996; National Council of Teachers of Mathematics, 2000). The National Council of Teachers of Mathematics (2000), for example, recommended that students should develop the abilities to "select and use appropriate statistical methods to analyze data" (p. 178) throughout Grades PreK-8. This included attaining proficiency in determining and applying the mean, median, and mode by the end of Grade 8.

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Practicing teachers' perspectives on a set of mathematics education research reports are described. Data were gathered through e-mail messages, group discussions, and questionnaires.Teachers identified positive influences of research on practice aligned with some of the strands of proficient mathematics teaching identified by Kilpatrick, Swafford, and Findell (2001).Teachers also gave negative critiques of the ability of research to influence practice aligned with Kennedy's (1997) discussion of historical factors underlying the gap between educational research and practice. The variety of perspectives documented provides some empirical ground for informing actions in the areas of teacher education and research.

Undergraduate research is increasingly prevalent in many fields of study, but it is not yet widespread in mathematics education. We argue that expanding undergraduate research opportunities in mathematics education would be beneficial to the field. Such opportunities can be impactful as either extracurricular or course-embedded experiences. To help readers envision directions for undergraduate research experiences in mathematics education with prospective teachers, we describe a model built on a design-based research paradigm. The model engages pairs of prospective teachers in working with faculty mentors to design instructional sequences and test the extent to which they support children’s learning. Undergraduates learn about the nature of systematic mathematics education research and how careful analyses of classroom data can guide practice. Mentors gain opportunities to pursue their personal research interests while guiding undergraduate pairs. We explain how implementing the core cycle of the model, whether on a small or large scale, can help teachers make instructional decisions that are based on rich, qualitative classroom data.

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